Giants Coach Tom Coughlin reacts during the first half of Sunday's game in East Rutherford, N.J. (AP photo)

EAST RUTHERFORD, N.J. — The New York Giants are still alive in the NFC East.

Realistically, their playoff hopes suffered a major setback in a 24-21 loss to the Dallas Cowboys on Sunday.

Tony Romo threw two touchdown passes and led a drive that set up Dan Bailey’s 35-yard field goal on the final play, ending the Giants’ four-game winning streak.

“We have a five-game schedule left,” coach Tom Coughlin said after the Giants (4-7) come up short.

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“Every game is critical. We want to prepare and work as hard as we possibly can, stay together and try and win football games. We lost a game we were all excited about having a chance to win. It’s gone. Let’s go win five games and give ourselves a chance to hold our heads up high.”

The victory moved the Cowboys (6-5) into a first-place tie with idle Philadelphia in the NFC East with five games left.

It left the Giants wondering about what they gave away in two losses to Dallas.

The latest defeat left the Giants little margin for error. They need to win the final five games, and get a lot of help.

“We knew we had to win this game to give ourselves a chance and keep the dream alive as coach Coughlin said,” said Terrell Thomas, who has guaranteed a win earlier in the week.

“We’ll see what happens, but right now we’re a team that lost another game in the division.”

Romo hit two third down passes on the 14-play drive that covered the final 4:45 after New York tied the game on a 4-yard touchdown pass from Eli Manning to Louis Murphy Jr., and a 2-point conversion run by Andre Brown.

Romo hit Jason Witten on TDs of 20 and 2 yards, and Dallas got a defensive touchdown on a 50-yard fumble return by Jeff Heath.

The Giants, seeking to become the second NFL team to win five straight after losing the first six, rallied over the past month to get into position to challenge for a playoff spot. They knew this was a key game because they had lost to Dallas in the season opener after turning over the ball six times.

After another loss to the Cowboys, the Giants face a tough battle to remain relevant in the playoff picture.

“Our mindset is that we’ve got to win five,” Manning said. “We have five games left and we have to win every one. That’s the only way to possibly give us a chance. We don’t know if that’s going to be good enough, but we know that’s the only way.”

The Cowboys faced their own challenges after a blowout loss to New Orleans before a bye week.

Romo and his team answered to end a week in which owner Jerry Jones said coach Jason Garrett would return next season.

True to form, New York tried another comeback after falling behind 21-6 in the third quarter.

But Romo took it from the Giants on the final drive that started at the Dallas 20 on a cold and blustery day. He hit Dez Bryant on a 19-yard pass on third-and-8 and added throws of 17 yards to Miles Austin and 13 to Cole Beasley, the latter on third-and-10 from the New York 28.

With the wind howling, a long field goal would have been tough. Instead, that play gave Dallas a first down at the 15 and Bailey converted after Romo took a couple of kneel-downs.

“Everyone understood how important the game was for both teams,” Romo said. “They won four in a row to put themselves back into position. They had a home game. I could tell by their words leading up to it that they were confident. That’s what makes the game great. It was a big buildup, but we understood that the game was going to be played on Sunday.”

The Giants’ tying drive was kept alive by a 22-yard pass from Manning to Victor Cruz on third-and-8 from the Dallas 27. Before that, the Cowboys seemingly took control with a 65-yard drive Romo capped with his second touchdown pass to Witten.

The drive continued because of a roughing-the-passer penalty against Mathias Kiwanuka on a play that Beasley fumbled after a catch at the Giants 20 and New York recovered.

Manning’s 27-yard pass to tight end Brandon Myers brought New York within 21-13. The final 10 yards were covered after safety Jeff Heath and linebacker Bruce Carter failed to touch Myers after he fell catching the ball. He got up and scored.

The Giants handed the Cowboys the season opener, committing six turnovers in a 36-31 loss. Two of those miscues were returned for touchdowns and two others led to 10 points.

New York continued that pattern in the rematch.

Cruz caught a pass near midfield and had the ball stripped by Orlando Scandrick. Heath picked it up and had a clear path to the end zone.

The fumble return started a run of four straight scores.

Manning hit Rueben Randle on passes of 21 and 22 yards to set up Josh Brown’s 21-yard field goal. Romo sandwiched passes of 14 and 17 yards to running back DeMarco Murray and Lance Dunbar around a 30-yard run by Murray on the next drive, setting up a 20-yard TD pass to a wide-open Witten.

Runs of 9 and 37 yards by Brandon Jacobs on consecutive plays got New York to the Dallas 4, but it settled for another short field goal.